Folding a list right and left using cons and nil results in the identity and reverse functions

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keywords: cons, fold, fold left, fold right, folding, foldl, foldleft, foldr, foldright, functional programming, haskell, identity, left fold, list, nil, recursion, reverse, right fold, tail recursion

Transcript

1. ∶ / \ 1 ∶ / \ 2 ∶ / \ 3 ∶ / \ 4 ‥ / \ ‥ 4 / \ ‥ 3 / \ ‥ 2 / \ [ ] 1 ∶ / \ 4 ∶ / \ 3 ∶ / \ 2 ∶ / \ 1 4 ∶ (3 ∶ 2 ∶ 1 ∶ ) ∶ / \ 1 ∶ / \ 2 ∶ / \ 3 ∶ / \ 4 1 : (2 : 3 : 4 : ) (( ‥1 ‥2 )‥3 )‥4 var acc = [ ] foreach(x in xs) acc = acc ‥x) return acc ∶ ‥ = [1 , 2 , 3 , 4 ] ∶ = = λ. λ. ∶ ‥ = = λ. λ. ∶ ∷ → → → → → = : = ∷ → → → → → = : = ∶ = λ. λ. ∶ ‥ = λ. λ. ∶ ‥ = ∶ ℎ = ∶ / \ ℎ . . / \ ℎ equivalent to [4 , 3 , 2 , 1 ] [1 , 2 , 3 , 4 ] > id = foldr (:) [] > rev = foldl (flip (:)) [] > id [1,2,3,4] [1,2,3,4] > rev [1,2,3,4] [4,3,2,1] > id = foldr (\x y -> x:y) [] > rev = foldl (\x y -> y:x) [] > id [1,2,3,4] [1,2,3,4] > rev [1,2,3,4] [4,3,2,1] : ∶ ℎ ∶ ℎ : ∶ ℎ ℎ var acc = e foreach(x in xs) acc = f (acc, x) return acc folding a list right and left using Cons and Nil results in the identity and reverse functions